Reputation
3,525
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 7 25
Impact
~37k people reached

14h
comment FullSimplify on TransformedDistribution
TransformedDistribution does not ever return a mathematical expression. Rather, it returns a meaningless black box: EITHER the very same thing you entered, namely TransformedDistribution[ blah] ... OR in simple well-known cases, it might return another black box e.g. TransformedDistribution[Exp[u], u \[Distributed] NormalDistribution[a, b]] will return the black box: LogNormalDistribution[a, b]. These are not mathematical expressions: they are just named black boxes.
14h
comment FullSimplify on TransformedDistribution
No - FullSimplify is doing nothing here. TransformedDistribution[a x, x dist UniformDistribution[{r,s}]] returns itself UniformDistribution[{a r, a s}].
14h
comment FullSimplify on TransformedDistribution
Given dist = TransformedDistribution[ blah ], what do you think FullSimplify[ dist ] should return? Why is it a meaningful thing to ask for? If you were to ask Mma to FullSimplify[ PDF[dist,x] ] ... well, that makes sense because you are full simplifying an expression. But TransformedDistribution[ blah ] is just a black box -- it not an expression, so how can you FullSimplify it ? [ This is separate to the fact that FullSimplify gives weird output here. ]
Aug
12
comment Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?
... which really highlights the difficulty of providing a general solution to such problems. The number of named special distributions is tiny compared to the number of common functional forms .. and even if one just wishes to restrict focus on named cases, how does one deal with $X^2$ or ratios of common forms, or truncated or censored functions of common forms, or shifted cases, or ...
Aug
12
comment Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?
There are infinitely many distributions ... (and thus also infinitely many possible matches)
Aug
12
comment Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?
> "In fact, I don't know what the correct answer is," .... ///////////// I like your new example. It is the pdf of $Y = 2-X$ where $X \sim Pareto(1, 7/10)$. Not sure it would be easy to do that automagically, however.
Aug
12
comment Distribution over the product of three, or n, independent Beta random variables
Very nice indeed to have a general solution from the Handbook of Beta Distribution -- I would go further and say that your answer not only constructs the pdf of the product of Beta random variables without the need of an add-on package, ... it does so without needing Mathematica either.
Aug
12
revised Distribution over the product of three, or n, independent Beta random variables
Changed generic x to x_i
Aug
12
revised Distribution over the product of three, or n, independent Beta random variables
added 2 characters in body
Aug
12
comment Distribution over the product of three, or n, independent Beta random variables
Applying FunctionExpand returns the same MeijerG function. I might add that it appears tractable for most of the domain ... but trying to plot it for $x$ close to 1 becomes very slow (which is also why that is 'left out' in the diagram above).
Aug
12
answered Distribution over the product of three, or n, independent Beta random variables
Aug
12
comment Distribution over the product of three, or n, independent Beta random variables
@Edmund good luck with that.
Jul
14
awarded  Popular Question
Jul
1
awarded  Good Answer
May
21
awarded  Good Question
Apr
28
comment how to calculate the covariance of sample central moments
You may have to refresh the browser window to see the update ...
Apr
28
comment how to calculate the covariance of sample central moments
I don't think R code will go down very well here. Suggest convert that to Mathematica code if you want some help with the simulation ...
Apr
28
revised how to calculate the covariance of sample central moments
Added requested result
Apr
28
comment how to calculate the covariance of sample central moments
I think you will need to show us your simulation to comment further on that component. I have added $Cov(\frac{s_1}{n}, m_3)$ to the above.
Apr
28
comment how to calculate the covariance of sample central moments
@BobHanlon The user's input is not a data set, but rather a symbolic statistic such as the sample variance which is itself a random variable. CentralMoment[list] does something very different.